منابع مشابه
Permutation codes
There are many analogies between subsets and permutations of a set, and in particular between sets of subsets and sets of permutations. The theories share many features, but there are also big differences. This paper is a survey of old and new results about sets (and groups) of permutations, concentrating on the analogies and on the relations to coding theory. Several open problems are describe...
متن کاملRemoteness of permutation codes
Let X be a finite set of ‘points’ and d be a metric on X which takes integral values. For any v ∈ X and t ≥ 0, we refer to the set Bt(v) = {u ∈ X : d(u, v) ≤ t} as the ball of radius t centered at v, and we denote the minimum (maximum, respectively) volume of a ball with radius t in X as V min t (V max t ). Let C ⊆ X, C 6= ∅ be a code, i.e. a set of points, which we will refer to as codewords. ...
متن کاملOn optimal permutation codes
Permutation codes are vector quantizers whose codewords are related by permutations and, in one variant, sign changes. Asymptotically, as the vector dimension grows, optimal Variant I permutation code design is identical to optimal entropy-constrained scalar quantizer (ECSQ) design. However, contradicting intuition and previously published assertions, there are finite block length permutation c...
متن کاملRepresenting group codes as permutation codes
Given an abstract group G, an N dimensional orthogonal matrix representation G of G, and an “initial vector” x ∈ R , Slepian defined the group code generated by the representation G to be the set of vectors Gx. If G is a group of permutation matrices, the set Gx is called a “permutation code”. For permutation codes a ’stack algorithm’ decoder exists that, in the presence of low noise, produces ...
متن کاملSpace Time Codes from Permutation Codes
A new class of space time codes with high performance is presented. The code design utilizes tailor-made permutation codes, which are known to have large minimal distances as spherical codes. A geometric connection between spherical and space time codes has been used to translate them into the final space time codes. Simulations demonstrate that the performance increases with the block lengths,...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2010
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2009.03.044